Make dot consistently return zero on empty arrays (#1494)

Author: dkarrasch

src/generic.jl

@@ -986,7 +986,8 @@ function dot(x::AbstractArray, y::AbstractArray)
         throw(DimensionMismatch(lazy"first array has length $(lx) which does not match the length of the second, $(length(y))."))
     end
     if lx == 0
-        return dot(zero(eltype(x)), zero(eltype(y)))
+        # make sure the returned result equals exactly the zero element
+        return zero(dot(zero(eltype(x)), zero(eltype(y))))
     end
     s = zero(dot(first(x), first(y)))
     for (Ix, Iy) in zip(eachindex(x), eachindex(y))

src/symmetric.jl

@@ -520,7 +520,7 @@ for (T, trans, real) in [(:Symmetric, :transpose, :identity), (:(Hermitian{<:Uni
             if n != size(B, 2)
                 throw(DimensionMismatch(lazy"A has dimensions $(size(A)) but B has dimensions $(size(B))"))
             end
-
+            iszero(n) && return $real(zero(dot(zero(eltype(A)), zero(eltype(B)))))
             dotprod = $real(zero(dot(first(A), first(B))))
             @inbounds if A.uplo == 'U' && B.uplo == 'U'
                 for j in 1:n

test/matmul.jl

@@ -676,23 +676,24 @@ end
     @test dot(Z, Z) == convert(elty, 34.0)
 end
 
-dot1(x, y) = invoke(dot, Tuple{Any,Any}, x, y)
-dot2(x, y) = invoke(dot, Tuple{AbstractArray,AbstractArray}, x, y)
 @testset "generic dot" begin
+    dot1(x, y) = invoke(dot, Tuple{Any,Any}, x, y)
+    dot2(x, y) = invoke(dot, Tuple{AbstractArray,AbstractArray}, x, y)
     AA = [1+2im 3+4im; 5+6im 7+8im]
     BB = [2+7im 4+1im; 3+8im 6+5im]
     for A in (copy(AA), view(AA, 1:2, 1:2)), B in (copy(BB), view(BB, 1:2, 1:2))
         @test dot(A, B) == dot(vec(A), vec(B)) == dot1(A, B) == dot2(A, B) == dot(float.(A), float.(B))
-        @test dot(Int[], Int[]) == 0 == dot1(Int[], Int[]) == dot2(Int[], Int[])
-        @test_throws MethodError dot(Any[], Any[])
-        @test_throws MethodError dot1(Any[], Any[])
-        @test_throws MethodError dot2(Any[], Any[])
-        for n1 = 0:2, n2 = 0:2, d in (dot, dot1, dot2)
-            if n1 != n2
-                @test_throws DimensionMismatch d(1:n1, 1:n2)
-            else
-                @test d(1:n1, 1:n2) ≈ norm(1:n1)^2
-            end
+    end
+    @test dot(Int[], Int[]) == 0 == dot1(Int[], Int[]) == dot2(Int[], Int[])
+    @test dot(ComplexF64[], Float64[]) === dot(ComplexF64[;;], Float64[;;]) === zero(ComplexF64)
+    @test_throws MethodError dot(Any[], Any[])
+    @test_throws MethodError dot1(Any[], Any[])
+    @test_throws MethodError dot2(Any[], Any[])
+    for n1 = 0:2, n2 = 0:2, d in (dot, dot1, dot2)
+        if n1 != n2
+            @test_throws DimensionMismatch d(1:n1, 1:n2)
+        else
+            @test d(1:n1, 1:n2) ≈ norm(1:n1)^2
         end
     end
 end

test/symmetric.jl

@@ -470,6 +470,10 @@ end
                 @test dot(symblockmu, symblockml) ≈ dot(msymblockmu, msymblockml)
                 @test dot(symblockml, symblockmu) ≈ dot(msymblockml, msymblockmu)
                 @test dot(symblockml, symblockml) ≈ dot(msymblockml, msymblockml)
+
+                # empty matrices
+                @test dot(mtype(ComplexF64[;;], :U), mtype(Float64[;;], :U)) === zero(mtype == Hermitian ? Float64 : ComplexF64)
+                @test dot(mtype(ComplexF64[;;], :L), mtype(Float64[;;], :L)) === zero(mtype == Hermitian ? Float64 : ComplexF64)
             end
         end